[{"_1":2,"_64":-5,"_65":-5},"loaderData",{"_3":4,"_33":34,"_62":-5,"_63":-5},"root",{"_5":-5,"_6":-5,"_7":8,"_20":-5,"_21":22,"_23":24,"_27":28},"user","shoppingCartId","shoppingCart",{"_9":10,"_11":12,"_13":14,"_15":16,"_17":18,"_19":12},"count",0,"free",true,"updatedAt","2026-01-09T12:55:21.432Z","paymentGateway","STRIPE","cartItems",[],"loading","toast","locale","en","constants",{"_25":26},"paypalClientId","AX53Cwz8jR6rVVzzZiZNWWXl0dGagi-GZrjG-S3Ua14E5nrKMn7DxDQ730O4R8LusLPp49ALn6aRVaEy","publishers",{"_29":30,"_31":32},"companies",[],"universities",[],"routes/_store+/_readers+/email_author.$slug/route",{"_35":36,"_61":-5},"book",{"_37":38,"_39":40,"_41":42,"_43":44,"_45":46,"_47":48},"id","Z2lkOi8vbGVhbnB1Yi9TdG9yZTo6Qm9va1Byb2R1Y3QvNjg2NTM","title","A Primer in Optimization","state","published","contactAuthorMethod","email","aboutText","

This tiny book presents the theory behind Karush-Kuhn-Tucker (KKT) conditions and how to solve minimization and maximization problems for differentiable functions defined on Rⁿ subject to a finite number of equality and inequality constraints. I tried to explain KKT conditions and duality beyond just solving the Lagrangian. I worked on direct explanations about the Hyperplane Separation Theorem, Farkas' Lemma, and the Envelope Theorem to connect mathematical notions to well-known micro results such as Roy's Identity and Shepard's Lemma for a straightforward interpretation of KKT multipliers as \"shadow prices\" and how changes in budgets and prices affect optimal decisions.

The goals are:

Cover what I consider are some gaps between Varian (1992) and/or Jehle (2011) compared to Mas-Colell (1995).
Provide a concise reference for students by presenting the results using consistent notation and terminology.
Provide a basis for more advanced topics in optimization, such as convex analysis and variational calculus.

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